Question

Solve please
$({a + b + c})^{3}$

Answer 1

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→ [ a + b + c ]³ = [ a + b + c ][ a + b + c ][ a + b + c ]

→ A little knowledge on Combinatorics can help you live at Peace !!

• Each Term of the Expansion occurs so that the overall Degree is '3' :
 

♦  Fix : 'a' at the first place :
     • We got : a² ; ac ; bc ; ab ; b² ; c² 

→ Similarly, 
 We fix : 'b' and 'c' at the first places to get the rest terms :

=> [ a + b + c ]³ = aa² + ab² + ac² + aab + aac + abc + ba² + bb² + bc² + bab + bac + bbc + ca² + cb² + cc² + cab + cbc + cac 

• Grouping them altogether :
$[ a + b + c ]^3 = a^3 + b^3 + c^3 + 2a^2b + 2a^2c + 2ab^2 + 2ac^2 + 2b^2c + 2bc^2 \\ + 3abc$
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♦ However, notice that. it's the very same concept as :
  -> [ a + b + c ]³ = [ a + b + c ][ a + b + c ]²
                          = [ a + b + c ][ a² + b² + c² + 2ab + 2bc + 2ca ]

→ And then you expand all that stuff to get what you needed ^^"
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→ There's many more ways like ... using Binomial Expansion and stuffs
→ Ping me if you're interested ^^"